I really like creating patterns on my 4x4x4 dice, so I got here up with the thought to create the next sample:
- all sides have a diagonal sample, that means one thing like
1234
2345
3456
4561
- all sides comprise all colours
I used to be capable of create such a sample with a whole lot of ‘heavy considering’ by first making a draft on a sheet of paper – hoping the sample I selected was doable – after which fixing the dice step-by-step (2×2 facilities first, then edges, then apply 3x3x3 fixing):
Note 1: On my first try I drafted an unsolvable sample, however I used to be capable of resolve this be swapping the 4 corners that aren’t a part of the primary diagonals.
Note 2: Since all sides has 7 diagonal strains, clearly 1 colour has to seem in 2 strains. I quickly came upon that it isn’t potential to create the diagonals in a approach, in order that at all times the other corners which aren’t a part of the primary diagnol line have the identical colour. So I made a decision to at all times reuse the primary diagonal line on one of many corners… (e.g. View 1, Top Face, Yellow essential diagonal, with 1 white and 1 yellow different nook)
My query now could be:
Is there a better strategy to create this sample (or a similiar one which fulfills the necessities) with an algorithm?
Or the opposite approach round: Is there a simple strategy to clear up this sample again to regular?
And lastly: Is my notice above (with the two corners) appropriate?